A single-photon source is a device that generates light pulses having only one photon, or that generates light pulses in a manner that makes it possible to isolate a single photon in one of the light pulses without the use of attenuation. Single-photon sources are used in a number of different applications, such as metrology, where sensitive measurements are necessary. More recently, single-photon sources are being investigated as light sources for quantum cryptography, and in particular quantum key distribution (QKD) systems.
QKD involves establishing a key between a sender (“Alice”) and a receiver (“Bob”) by using weak (e.g., 1 photon per pulse) optical signals (“quantum signals”) transmitted over a “quantum channel.” The security of the key distribution is based on the quantum mechanical principle that any measurement of a quantum system in unknown state will modify its state. As a consequence, an eavesdropper (“Eve”) that attempts to intercept or otherwise measure the quantum signal will introduce errors into the transmitted signals, thereby revealing her presence.
The general principles of quantum cryptography were first set forth by Bennett and Brassard in their article “Quantum Cryptography: Public key distribution and coin tossing,” IEEE Proceedings of the International Conference on Computers, Systems and Signal Processing, Bangalore, India, Dec. 10-12, 1984, pp. 175-179. Specific QKD systems are described in the publication by C. H. Bennett et al., entitled “Experimental Quantum Cryptography,” J. Cryptology 5: 3-28 (1992), in the publication by C. H. Bennett, entitled “Quantum Cryptography Using Any Two Non-Orthogonal States”, Phys. Rev. Lett. 68 3121 (1992), and in U.S. Pat. No. 5,307,410 to Bennett (the '410 patent). The general process for performing QKD is described in the book by Bouwmeester et al., “The Physics of Quantum Information,” Springer-Verlag 2001, in Section 2.3, pages 27-33.
Most conventional QKD systems employ a multi-photon source, such as a laser, and attenuate multi-photon pulses to achieve single-photon quantum signals (pulses), i.e., light pulses having a mean photon number μ≦1. This is called “weak coherent pulse” or WCP QKD. Multi-photon sources have been used to validate the compatibility of quantum communication protocols with an existing optical network. However, the pulses from an attenuated multi-photon source obey a Poisson distribution, which poses inherent difficulties for a commercially viable QKD system. First, most (typically, over ˜90%) of the pulses do not contain any photons, which severely limits the transmitted data rate. At the other extreme, some of the pulses (about 10% of useful pulses) are multi-photon pulses. This allows for an eavesdropper to either intercept a pulse and analyze one of the photons in the pulse to extract information while allowing the other photons in the pulse to proceed to the other QKD station, or to re-transmit the pulse without error.
Some single-photon sources are based on spontaneous parametric down conversion, whereby two entangled photons—a signal photon and an idler photon—are emitted. A single-photon source based on spontaneous parametric down-conversion is characterized by a wide spectral bandwidth. In a QKD system that includes an optical fiber link, the optical fiber causes a timing spread amongst the signal photons of different frequency during their transmission over the optical fiber. This spreading is called “chromatic dispersion.” Accordingly, single-photons with wide spectral bandwidths are not particularly useful in a practical (e.g., commercially viable) QKD system.
The precise spectrum of the down-converted photons depends on the spectral characteristics of the pump laser and the phase-matching conditions of the nonlinear media (crystal) used to form the photons. The spectrum of photons generated by spontaneous parametric down conversion is governed by group velocity mismatch and is normally a few nanometers or broader. Also, the center frequency of the emitted photons varies because the frequencies of the emitted photons can be any two frequencies that sum to the pump frequency used to pump the non-linear medium. The sum frequency spectrum of the signal and idler photons is governed by the pump spectrum and can be very narrow if a continuous-wave (CW) pump is used, while the individual photon spectrum is governed by the group velocity mismatch (of the order of 1 ps or so) and usually is broad (of the order of 10 nm or so).
The spectral bandwidth of single-photon quantum signals has an impact on the performance of a QKD system. In particular, time domain spreading of the photon's spectral bandwidth requires the use of a wider gating pulse for both detection and modulation elements. This results in an increase dark-count rate (DCR) (usually, DCR is linearly proportion to the gating pulse width), which lowers the signal to noise ratio (SNR) and translates into a shorter transmission distance for the QKD system.
For example, chromatic dispersion of a typical telecommunications single-mode (optical) fiber (SMF) at 1550 nm wavelength is D(1550 nm)=17 ps/nm·km. Assume that the single-photon source is used to generate the quantum signals and has a spectral bandwidth of ˜3 nm. After quantum signal propagation through 100 km of SMF fiber, quantum signal spreading in time domain will be D(1550)=5.1 ns. This would require a gating signal pulse width of >5.1 ns, which results in a DCR increase of multiple times as compared to the original (non-dispersed) quantum signal.
There are a few approaches to solving this problem, though each has an unfortunate disadvantage. For example, one approach is to filter the quantum signal bandwidth to narrow its spectrum for transmission. However, this approach has the disadvantage of a significantly decreased efficiency of the SPS, which, in turn reduces the QKD transmission distance. Another approach is to perform chromatic dispersion compensation at the receiving QKD station. However, this inevitably introduces loss, which reduces the QKD transmission distance as well.